Related papers: Quantum Circuits for Sparse Isometries
We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one where only a polynomially small, a priori…
Quantum computations are expressed in general as quantum circuits, which are specified by ordered lists of quantum gates. The resulting specifications are used during the optimisation and execution of the expressed computations. However,…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
The problem of simulatability of quantum processes using classical resources plays a cornerstone role for quantum computing. Quantum circuits can be simulated classically, e.g., using Monte Carlo sampling techniques applied to…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
Modular quantum computing architectures require error correction schemes that remain effective in the presence of noisy inter-processor operations. As such, minimizing the number of such operations on logical circuits partitioned across…
Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary…
Two schemes are presented that mitigate the effect of errors and decoherence in short depth quantum circuits. The size of the circuits for which these techniques can be applied is limited by the rate at which the errors in the computation…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
A minimal depth quantum circuit implementing 5-qubit quantum error correction in a manner optimized for a linear nearest neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that…
Overcoming the influence of noise and imperfections in quantum devices is one of the main challenges for viable quantum applications. In this article, we present different protocols, which we denote as "superposed quantum error mitigation",…
Decoherence-free subspaces allow for the preparation of coherent and entangled qubits for quantum computing. Decoherence can be dramatically reduced, yet dissipation is an integral part of the scheme in generating stable qubits and…
Calibration of quantum gates is a necessary hurdle to overcome on the way to a reliable quantum computer. In a recent paper, a protocol called Gate Set Calibration protocol (GSC) has been introduced and used to learn coherent errors from…
The decomposition of multiport interferometers is a fundamental tool in quantum optics and computing. This note aims to serve as a concise reference for performing the decomposition according to the most common design approaches, offering a…
The synthesis of a quantum circuit consists in decomposing a unitary matrix into a series of elementary operations. In this paper, we propose a circuit synthesis method based on the QR factorization via Householder transformations. We…
Geometric phases induced in quantum evolutions have built-in noise-resilient characters, and thus can find applications in many robust quantum manipulation tasks. Here, we propose a feasible and fast scheme for universal quantum computation…
We address the question of efficient implementation of quantum protocols, with small communication and entanglement, and short depth circuit for encoding or decoding. We introduce two new methods to achieve this, the first method involving…
In recent years, the quantum computing community has seen an explosion of novel methods to implement non-trivial quantum computations on near-term hardware. An important direction of research has been to decompose an arbitrary entangled…
Quantum hashing is a useful technique that allows us to construct memory-efficient algorithms and secure quantum protocols. First, we present a circuit that implements the phase form of quantum hashing using $2^{n-1}$ CNOT gates, where n is…